1. MUSIC THEORY 2.0 Dmitri Tymoczko Princeton University
MUSIC THEORY 2.0
Dmitri Tymoczko
Princeton University 1

2.
THREE THINGS ABOUT ME
I am most interested in modern and broadly tonal music:
Debussy
Stravinsky
1940s Messiaen
Shostakovich
Jazz (especially after WWII)
Rock
Minimalism and postminimalism
World music
But, many of the things I say will be applicable to atonal music as well.

3.
THREE THINGS ABOUT ME
I am mostly interested in symbolic musical data (scores) rather than audio.
I am interested in composer or analyst cognition rather than listener perception.
Ideas we might have to work to hear
Many great composers are intellectual
Discovering new ways for music to be
I like understanding what other composers are doing, and discovering new ideas for writing music.

4. TWO ANALYSES? http://dmitri.tymoczko.com
Future versions of this talk may begin with two brief analyses: the analysis of Des pas sur la neige from Debussy’s Preludes and Chopin Prelude in E minor.
These can be found in Chapters 8 and 9 of “A Geometry of Music.”

5. SOME IDEAS A fast tour through a lot of material.
SOME IDEAS
A fast tour through a lot of material.
The main point: our most general way of thinking about musical objects (set theory) is incomplete:
Scales
Voice leading.
More generally, to suggest that there is room for new ideas in music!

6.
FIRST IDEA
Two-leveled hierarchy, with progressions happening at the level of the chord and the scale.

7.
SECOND IDEA
At each level of the hierarchy, we can identify two different kinds of structure.

8.
THIRD IDEA
The best way to test a theoretical idea is to experiment on yourself.

9.
FOURTH IDEA
We can formalize the motion between objects using the concept of a voice leading:
A voice leading is a collection of paths in pitch class space.
It shows how the notes of one chord move to the notes of another (ignoring octaves).
“C major moves to F major by keeping the root constant, moving the third up by semitone, and moving the fifth up by two semitones.”

10.
FIFTH IDEA

11.
FIFTH IDEA

12. SIXTH IDEA Scales serve two different functions:
SIXTH IDEA
Scales serve two different functions:
They act as large or macro harmonies that control the pitches we hear.
They provide a measure of musical distance, the scale step.

13. SEVENTH IDEA Evenness is a fundamental attribute of musical objects.
SEVENTH IDEA
Evenness is a fundamental attribute of musical objects.
At the level of the chord: it allows chords to be connected to their transpositions by small voice leadings.
At the level of the scale: it ensures that the scalar measure of musical distance is roughly equal to the log-frequency measure.
Very uneven objects are also interesting.

14.
EIGHTH IDEA
Approximateness: if you can do something with a chord, then you can do something like it with a nearby chord.

15.
EIGHTH IDEA
Approximateness: if you can do something with a chord, then you can do something like it with a nearby chord.

16.
NINTH IDEA
If you can do something in one scale, you can do something similar in other scales.

17.
TENTH IDEA
Consider voice leadings to be related when they differ only by a transpositional factor.
the center-of-mass coordinate system

18.
TENTH IDEA

19.
ELEVENTH IDEA

20.
Thank you! 20